I had a hunch that it must somehow be "me" and not my ISP, so I replace ALL of my network gear with Ubiquiti stuff. I got a UniFi USG (handles actual routing), UniFi Switch (US-8-150W), UniFi AP AC Pro (Wireless AP), CloudKey (runs the software that powers all this, but it's not strictly needed, you can run it on your PC/Mac as well just to setup things and it doesn't need to be running 100% of the time).
Since I've done this I've had ZERO disconnects. Not a single one. No WiFi problems either. I'm not sure if it would fix what you're experiencing, but I thought I'd share my experience.